Physics-Informed Neural Networks (PINNs) embed the partial differential equations (PDEs) governing the system under study directly into the training of Neural Networks, ensuring solutions that respect physical laws. While effective for single-system problems, standard PINNs scale poorly to datasets containing many realizations of the same underlying physics with varying parameters. To address this limitation, we present a complementary approach by including auxiliary physically-redundant information in loss (APRIL), i.e. augment the standard supervised output-target loss with auxiliary terms which exploit exact physical redundancy relations among outputs. We mathematically demonstrate that these terms preserve the true physical minimum while reshaping the loss landscape, improving convergence toward physically consistent solutions. As a proof-of-concept, we benchmark APRIL on a fully-connected neural network for gravitational wave (GW) parameter estimation (PE). We use simulated, noise-free compact binary coalescence (CBC) signals, focusing on inspiral-frequency waveforms to recover the chirp mass $\mathcal{M}$, the total mass $M_\mathrm{tot}$, and symmetric mass ratio $\eta$ of the binary. In this controlled setting, we show that APRIL achieves up to an order-of-magnitude improvement in test accuracy, especially for parameters that are otherwise difficult to learn. This method provides physically consistent learning for large multi-system datasets and is well suited for future GW analyses involving realistic noise and broader parameter ranges.

翻译：物理信息神经网络（PINNs）将支配所研究系统的偏微分方程（PDEs）直接嵌入神经网络的训练中，从而确保解符合物理定律。虽然标准PINNs在单一系统问题上有效，但其难以扩展到包含同一基础物理但参数不同的多个实现的数据集。为应对这一局限，我们提出一种互补方法，即在损失函数中加入辅助物理冗余信息（APRIL），亦即通过利用输出间精确物理冗余关系的辅助项来增强标准监督输出-目标损失。我们从数学上证明，这些项在保持真实物理极小值的同时，能重塑损失函数的景观，从而改善向物理一致解的收敛。作为概念验证，我们在一个用于引力波（GW）参数估计（PE）的全连接神经网络上对APRIL进行了基准测试。我们使用模拟的、无噪声的致密双星并合（CBC）信号，重点关注旋进频率波形，以恢复双星系统的啁啾质量 $\mathcal{M}$、总质量 $M_\mathrm{tot}$ 和对称质量比 $\eta$。在此受控设置下，我们表明APRIL在测试准确度上实现了高达一个数量级的提升，特别是对于那些原本难以学习的参数。该方法为大型多系统数据集提供了物理一致的学习框架，非常适用于未来涉及真实噪声和更广参数范围的引力波分析。